Puzzles & Experiments

Experiment #1 Discovering Special Properties of Special Parallelograms

• Finding Shape Properties using Rulers and Tracing
  • "Discovering Geometry: An Inductive Approach" Serra, P. 311-312

Experiment #2 Midsegment Conjectures

• Shapes Within Shapes
  • "Discovering Geometry: An Inductive Approach" Serra, P. 773

Experiment #3 Quadrilateral Linkages

• The Pentagraph & Others
  • "Discovering Geometry: An Inductive Approach" Serra, P. 308

Experiment #4 Polygon Sum Conjectures

1. Draw a polygon onto a sheet of heaby paper. Cut the polygon and tear off its angles. On another sheet of paper, draw a line and a point on the line. Arrange the torn off angles around the point. Write a paragraph that explains how this activity demonstrates the Polygon Sum Conjecture for this polygon.

2. Draw several polygons that have four or more sides. In each, draw diagonals from a single vertex. Explain how the Polygon Sum Conjecture follows logically from the Triangle Sum Conjecture. Does the Polygon Sum Conjecture apply to concave polygons?

3. On a sphere, investigate the Polygon Sum Conjecture. Once you make a conjecture, explain how it is related to the Triangle Sum Conjecture on a sphere. Be sure to test your conjecture on the smallest and largest possible polygons.

"Discovering Geometry: An Inductive Approach" Serra, P. 281

Experiment #5 Straight Lines - The Parallelogram Pencil Box

• "How Math Works", Carol Vorderman, Reader's Digest P. 120-121

Experiment #6 Simple Shapes - Magic Wallet & Pentominoes

• "How Math Works", Carol Vorderman, Reader's Digest P. 128-129

Experiment #7 Quadrilaterals in Tangrams

• "A Problem Solving Approach to Mathematics", Billstein, P. 560
• Link to EMT 669 Student Page - Tangrams

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